**B. Mamporia**

## On the Ito Formula in a Banach Space

**abstract:**

If $(W_t)_{t\in[\,0,1]}$ is a Wiener process in an arbitrary
separable Banach space $X$, $\psi:[\,0,1]\times X\to Y$ is a continuous
function with values in another separable Banach space,
and $\psi$ has continuous Frechet derivatives $\psi'_t$, $\psi'_x$ and
$\psi_{xx}''$, then the Ito formula is obtained for $\psi(t,W_t)$.
\par The method is based on the concept of covariance operator and
a special construction of the Ito stochastic integral.